Zonal harmonic perturbations of an accurate reference orbit of an artificial satellite

Abstract

The theory developed in an earli er paper, for an accurate reference orbit of an artific ial satellite, is fi rs t slightly modified, so as to prepare the way for a treatment of zonal harmonic perturbations. Delaunay variables are next introduced , by means of certai n linear combinations of the action variables, along with their canonical conjugates. Application of the von Zeipel method then permits the calc ulation of the most important zonal harmonic perturbations. These ari se from the third , with coefficie nt 13, and the residual fourth, with coefficient 1. + 1~ . The accuracy of the secular and shortperiodic effects is through terms of order 1~ and that of the long-periodic e ffects is through terms of order h . Since the reference orbit itself, with its exac t secular terms, takes care of all but 0.5 per· cent of the de viation of the earth 's gr avitational fie ld from spherical symmetry, the overall secular accuracy of the final orbit surpasses that of other second order theories. T he results are compared with those of Kozai .